Check out Alicenine and One more time One more chance by Yamazaki Masayoshi. I would also recommend Moriyama Naotaro. (my favorite songs of Naotaro are さくら and 生きてることが辛いなら） Mori Tsubasa is good as well.

Etto... I enjoy LAST ALLIANCE so much, but it's more noisy. I also like Ikimono Gakari, like someone above said 8D Asian Kung-fu Generation is also great!

I don't know if you like this kind of music, but I loooove HIGH and MIGHTY COLOR (Haikara)! They're pretty awesome, it's the only band with a woman singing that sounds good to me. (Gee, my English is awful these days) And Haikara sings the third OP of the anime Bleach, "Ichirin no Hana" (my favourite Jsong EEEEEVER). Check it out!

BACK-ON has a lot of good alternative rock songs. They did many, many anime songs as well. Believer is a good one, as well as Chain and Sands of Time. Guitar Wolf I didn't like at first but I'm starting to get into it. I like their song "Venus Drive".